The graph below shows four straight lines, p, q, r, and s: graph of line p going through ordered pairs negative 2, negative 5 and 0, 3. graph of line q going through ordered pairs negative 1, negative 2 and 1, 6. graph of line r going through ordered pairs negative 1, negative 4 and 1, 4. graph of line s going through ordered pairs 0, negative 3 and 2, 5 which line is represented by the function f(x) = 4x - 3?

You are given the graph of four straight lines, P, Q, R, and S. You are asked to find which line corresponds to the function of f(x) = 4x - 3. The easiest way to answer this is to plug in the values of the coordiante points used for each graph.

f(x) = 4x - 3 = y
y = 4x - 3
for graph of line S we have the coordinates (0, -3) and (2, 5)
(0, -3)
-3 = 4(0) - 3
-3 = -3

(2,5)
5 = 4(2) - 3
5 = 8 - 3
5 = 5

So the answer is the graph of line S.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

f(-2) = -3f(1) = 6 . . . estimated from f(x) = (x+2)^2-3, which matches points on the graph (-1,-2) and (0, 1)

so the change in y-value for function f is (6 )) = 9.

the table tells us

g(-2) = 1g(1) = 31

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

The coordinates of point a right now is (-3,-1) you have to multiply these coordinates by a factor of 2 to get (-6,-2)